In its most basic form, a mechanical movement consists of a power source, gear train, escapement, oscillator, and indicator. The power source is typically a dropping weight for a clock or a main spring for a watch. The main spring is wound manually or via an auto-winding mechanism. Power in the form of torque is transmitted from the power source via the gear train to increase the angular velocity until it reaches the escapement. The escapement regulates the release of power into the oscillator. The oscillator is in essence a spring-mass system in the form of a pendulum for a clock or balance wheel with hairspring for a watch. It oscillates at a stable natural frequency which is used for timekeeping. As the oscillator amplitude decreases due to dissipative elements, the escapement regularly injects power into the system to compensate based on the state of the oscillator. At the same time, the escapement allows the gear train to move slightly which drives the indicator to display time.
The oscillator is a key component in mechanical movements due to its role in determining time rate. A conventional watch oscillator consists of a balance wheel and hairspring. The balance wheel is attached to the balance staff held in position by one or more bearings which also allows the subassembly to rotate. The typical hairspring follows an Archimedes spiral with equal spacing between each turning. The outer end of the hairspring is attached to a fixed point, and the inner end is attached to the balance staff. The resulting setup can be modeled as a linear spring-mass system with the balance wheel and hairspring providing the inertia and restoring torque, respectively. The hairspring will force the balance wheel into clockwise and counter-clockwise oscillatory rotations around its equilibrium position (or dead spot).
Some high-end mechanical movements consist of two oscillators which may or may not be driven by the same main spring. The two oscillators do not have direct mechanical connection and move independently. The gear train is designed such that the displayed time is the average of the two oscillators, thus averaging out any error in each individual oscillator.
The traditional hairspring with Archimedes spiral has different geometry for over-coil and under-coil where the balance wheel angular displacement is greater or less than its equilibrium position, respectively. This implies that oscillator system dynamic is asymmetric around its equilibrium position with different amplitudes for over-coil and under-coil. Typically watch escapement such as Swiss lever escapement uses asymmetric pallet action with different pallet steepness and moment arm to compensate for this asymmetry. However, this is an imperfect solution as the compensation is only partial.
The traditional twin-oscillator mechanical movement lacks direct mechanical connection between the two oscillators, implying that they do not have an efficient mean of synchronization. The lack of synchronization negatively affects movement accuracy and makes it more difficult to perform diagnostic traditionally based on the movement's acoustic signature.
Referring to FIG. 1, an oscillator 10 of a mechanical timepiece using a traditional single-coil hairspring 12 is illustrated. The traditional single-coil hairspring has only one end that is attached to the balance wheel. The geometry is based on the Archimedes spiral 12. The outer end of the spring 12 is attached to a fixed point via a stud 13, and the inner end of the spring 12 is attached to a balance staff 14 which rotates along with a balance wheel 11. Since the geometry of the hairspring 12 is different when it is in over-coil and under-coil, the dynamic of the oscillator 10 is asymmetric around its equilibrium position as depicted in FIG. 2. The equilibrium position or dead spot is a state or condition of the oscillator where the net torque acting on the balance wheel(s) is/are zero and the hairspring is relaxed. When the balance wheel leaves the equilibrium position, it stresses the hairspring. This creates a restoring torque which, when the balance wheel 11 is released, makes it return to its equilibrium position. As it has acquired a certain speed, and therefore kinetic energy, it goes beyond its dead spot until the opposite torque of the hairspring 12 stops it and obliges it to rotate in the other direction. Thus, the hairspring 12 regulates the period of oscillation of the balance wheel 11.
Turning to FIG. 2, the oscillation of the balance wheel 11 is charted. As the hairspring 12 coils in one direction about its equilibrium position, its amplitude 21 is different from the amplitude 22 when the hairspring 12 coils in the other direction.
In a conventional double escapement-oscillator design, the oscillators are effectively decoupled. Due to manufacturing tolerance, each oscillator has a slightly different natural frequency causing them to periodically shift into and out of phase. This contributes to the movement inaccuracy as each oscillator fights another to regulate the time. Furthermore, the design makes it difficult for a watchmaker to adjust the oscillators as conventional diagnostic tools measure a single oscillator's frequency, amplitude, and other performance criteria based on its acoustic signature. Having two out-of-phase oscillators mean that the acoustic signature is scrambled and difficult to decode.
There is a desire for an oscillator system that ameliorates some of the problems of traditional mechanical timepieces.